Increasing stability in an inverse problem for the acoustic equation

Author: Nagayasu Sei   Uhlmann Gunther   Wang Jenn-Nan  

Publisher: IOP Publishing

ISSN: 0266-5611

Source: Inverse Problems, Vol.29, Iss.2, 2013-02, pp. : 25012-25022

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Abstract

In this work, we study the inverse boundary value problem of determining the refractive index in the acoustic equation. It is known that this inverse problem is ill-posed. Nonetheless, we show that the ill-posedness decreases when we increase the frequency and the stability estimate changes from logarithmic type for low frequencies to a Lipschitz estimate for large frequencies.